The notion of an orthogonal polynomial ensemble generalizes many important point processes arising in random matrix theory, probability and combinatorics. The most famous example perhaps is that of the eigenvalue distributions of unitary invariant ensembles (such as GUE ) of random matrix theory. Remarkably, the study of fluctuations of these point processes is intimately connected to the study of Jacobi matrices. This talk will review our recent joint work with Maurice Duits exploiting this connection to obtain central limit theorems for orthogonal polynomial ensembles.